546 Dr. W. F. G. Swarm on the Pulse 



to the square root of the frequency *, a law which we shall 

 see can be made to follow from a slightly modified form of 

 the above theory in which the main part of the electron's 

 velocity exists in the y component. 



Although (16) cannot be the explanation of the photo- 

 electric effect, it is a formula to which the results should 

 approximate for very large values of co, and consequently 

 very small values of X, at any rate when we introduce u 

 factor X to allow for the absorption of more than one Planck 

 unit, so that it is well fitted to represent the facts for X 

 or 7 rays. Suppose, for example, we take \ = 5xl0~ 9 for 

 Xrays, and X as small as unity, we find u=l'3 x 10 9 , a value 

 approaching the right magnitude, and we shall presently see 

 that for these velocities the value of v would probably be 

 quite insignificant, though even if it were as great as u it 

 would not alter the order of magnitude of the velocity found. 

 It must be particularly remarked that our theory does not 

 involve a unitary structure for light, nor indeed does it 

 necessitate the introduction of the Planck unit at all. It 

 merely involves the idea that the electron requires a definite 

 amount of energy to set it free. The association of this 

 amount of energy with the Planck unit is not essential. 



On a view which considers that practically the whole initial 



velocity of the electrons set free by X rays or by <y rays takes 



place in the direction of the advancing wave, the difficultv 



becomes, not to explain the want of symmetry in the expulsion 



of the /3 rays, but the existence of any symmetry at all, to 



exp'ain in fact why any rays come out against the train. The 



difficulty may at once be met by assuming that the /3 rays, 



though they are all originally started in the same direction, 



are scattered by the material of the plate; and it is a significant 



fact that in a substance like lead, which we know scatters 



/3 rays much more than substances of low atomic weight, a want 



of symmetry of only 15 per cent, is found, for the /3 rays 



ejected by y rays, i. e. the scattering of the /3 rays is 



almost complete, while in a light atom like carbon the ejected 



{3 rays come out almost entirely in the direction of the 



emergent y rays. It would be interesting to see whether, in 



the case of very thin films of substances of heavy atomic 



weight, there was a more prominent asymmetry than in the 



case of thicker films. We should expect this, since if the film 



is very thin the scattering will be diminished. 



(3) Case where v is not small compared ivith n. — Let us 

 now turn to a consideration of the case where the velocity 

 with which the electrons emerge from the atom is not 

 * Richardson and Compton, Phil. Mag. xxiv. p. 575, Oct. 1912. 



